Mahdi Mohammadpour

Transmission efficiency and noise, vibration and harshness refinement of differential hypoid gear pairs

This article presents a combined multi-body dynamics and lubricated contact mechanics model of vehicular differential hypoid gear pairs, demonstrating the transient nature of transmission efficiency and noise, vibration and harshness performance under various driving conditions. The contact of differential hypoid gears is subjected to mixed thermo-elastohydrodynamic regime of lubrication. The coefficient of friction is obtained using an analytical approach for non-Newtonian lubricant shear and supplemented by boundary interactions for thin films. Additionally, road data and aerodynamic effects are used in the form of resisting torque applied to the output side of the gear pair. Sinusoidal engine torque variation is also included to represent engine order torsional input resident on the pinion gear. Analysis results are presented for New European Driving Cycle transience from low-speed city driving condition in second gear to steady-state cruising in fourth gear for a light truck. It is shown that the New European Driving Cycle captures the transmission efficiency characteristics of the differential hypoid gear pair under worst case scenario, with its underlying implications for fuel efficiency and emissions. However, it fails to address the other key attribute, being the noise, vibration and harshness performance. In the case of hypoid gears, the resultant noise, vibration and harshness characteristics can be particularly annoying. It is concluded that broader transient manoeuvres encompassing New European Driving Cycle are required for assessment, in order to obtain a balanced approach for transmission efficiency and noise, vibration and harshness performance. This approach is undertaken in this article, which is not hitherto reported in the literature.

Elastohydrodynamic lubrication of hypoid gear pairs at high loads

Differential hypoid gear pairs have been the mechanism of choice for high-torque capacity final drives in all forms of vehicles, at least since mid-19th century. Transmission efficiency as well noise and vibration concerns requires combined elastohydrodynamic and tooth contact analysis of hypoid gear teeth pairs through mesh. Although such analyses have been reported for general cases of elliptical point contact conjunctions with angled flow entrainment, they do not comply with the prevailing load and kinematic conditions in differential gears. In particular, teeth pair contacts are subject to significant loads of order of several kilo Newtons requiring solution to the elastohydrodynamic lubrication problem at such high loads. The current analysis reports solutions for rolling and sliding elastohydrodynamics of hypoid gear teeth pairs at realistic drive torques, not hitherto reported in literature.

Multiphysics Investigations on the Dynamics of Differential Hypoid Gears

Vehicular differential hypoid gears play an important role on the noise, vibration, and harshness (NVH) signature of the drivetrain system. Additionally, the generated friction between their mating teeth flanks under varying load-speed conditions is a source of power loss in a drivetrain while absorbing some of the vibration energy. This paper deals with the coupling between system dynamics and analytical tribology in multiphysics, multiscale analysis. Elastohydrodynamic lubrication (EHL) of elliptical point contact of partially conforming hypoid gear teeth pairs with non-Newtonian thermal shear of a thin lubricant film is considered, including boundary friction as the result of asperity interactions on the contiguous surfaces. Tooth contact analysis (TCA) has been used to obtain the input data required for such an analysis. The dynamic behavior and frictional losses of a differential hypoid gear pair under realistic operating conditions are therefore determined. The detailed analysis shows a strong link between NVH refinement and transmission efficiency, a finding not hitherto reported in literature.

Boundary Conditions for Elastohydrodynamics of Circular Point Contacts

The paper presents the solution of an elastohydrodynamic point contact condition using inlet and outlet lubricant entrainment with partial counter-flow. The inlet and outlet boundaries are determined using potential flow analysis for the pure rolling of contiguous surfaces. This shows that Swift–Stieber boundary conditions best conform to the observed partial counter-flow at the inlet conjunction, satisfying the compatibility condition. For the outlet region, the same is true when Prandtl–Hopkins boundary conditions are employed. Using these boundary conditions, the predictions conform closely to the measured pressure distribution using a deposited pressure-sensitive micro-transducer in a ball-to-flat race contact. Furthermore, the predicted conjunctional shape closely conforms to the often observed characteristic keyhole conjunction through optical interferometry. The combined numerical–experimental analysis with realistic boundary conditions described here has not hitherto been reported in the literature.

Effect of cylinder deactivation on the tribo-dynamics and acoustic emission of overlay big end bearings:

The paper presents an integrated tribo-dynamics analysis of elliptic bore overlay big end bearings of internal combustion engines. The analysis focuses on bearing stability, frictional power loss and acoustic emission from these bearings, particularly with cylinder deactivation with larger fluctuations in engine loading. The integrated approach represents a tribo-dynamics analysis, not hitherto reported in literature, particularly under cylinder deactivation. The analysis shows that cylinder deactivation makes marginal differences in parasitic frictional losses in engine bearing performance and any significant gain would depend on the brake specific fuel consumption. It is also shown that sufficient swept volume with retained residual exhaust gas charge within the deactivated cylinders can ensure bearing whirl stability. Partially deactivated engine configurations exhibit a lower average steady noise emission, but with a higher degree of transient content. This suggests that there would be a greater contribution to engine rumble with deactivated cylinders.

Transient mixed non-Newtonian thermo-elastohydrodynamics of vehicle differential hypoid gears with starved partial counter-flow inlet boundary

The paper presents solutions for transient mixed thermo-elastohydrodynamics of meshing differential hypoid gears of a vehicle under low speed urban driving and high speed cruising. Realistic gear meshing conditions, such as contact load including inertial effects are used, in line with engine power torque and wheel traction. This constitutes simultaneous solution of gear pair dynamics, non-Newtonian elastohydrodynamics as well as vehicle longitudinal inertial dynamics, an approach not hitherto reported in the literature. The important link between contact tribology and vehicle gearing dynamics is highlighted. It is also shown that gear teeth pairs are subjected to a starved inlet boundary condition, represented by realistic inlet flow analysis. These conditions lead to the formation of a thin lubricant film with non-Newtonian shear and with modest boundary interactions.

Dynamics and efficiency of planetary gear sets for hybrid powertrains

The paper presents a tribo-dynamic model for planetary gear sets of hybrid-electric-vehicle configurations. The model comprises a six degree-of-freedom torsional multi-body dynamic system, as well as a tribological contact model in order to evaluate the lubricant film thickness, friction and efficiency of the meshing gear teeth contacts. The tribological model takes into account the non-Newtonian, thermal-mixed elastohydrodynamic regime of lubrication. Analysis is performed for a hybrid electric C-segment vehicle. The simulated conditions correspond to cases of power supplied by either the engine or the electric motor. The results illustrate that in the electric motor drive mode, improved noise, vibration and harshness refinement would be expected, whereas better transmission efficiency is achieved in the internal combustion engine drive mode.

Effect of teeth micro-geometrical form modification on contact kinematics and efficiency of high performance transmissions:

Light weight, compactness and efficiency are key objectives in high performance vehicular transmission systems, which are subject to large variations in torque and power. Pitch line velocities of up to 52 m/s and teeth pair contact pressures of up to 3 GPa are routinely encountered under race conditions. Contact patch asymmetry due to angular misalignments between input and output shafts leads to the generation of high edge stress discontinuities on gear flanks, inducing fatigue spalling which affects system durability. Crowning is widely used as a palliative measure to mitigate these undesired effects. These problems can be further exacerbated by contact footprint truncation. The paper presents a new approach to modelling the kinematics and contact micro-geometry of meshing conjunctions of involute spur gears with profile and lead modifications. A time-efficient analytical method is presented to accurately determine the contact footprint and kinematics, leading to the solution of highly loaded non-Newtonian mixed thermo-elastohydrodynamic contact under the extreme prevalent conditions of high performance vehicular transmissions. The effect of tooth form modification on contact footprint truncation, contact kinematics and generated frictional power loss is investigated. This approach has not hitherto been reported in literature.

Targeted energy transfer and modal energy redistribution in automotive drivetrains

The new generations of compact high output power-to-weight ratio internal combustion engines generate broadband torsional oscillations, transmitted to lightly damped drivetrain systems. A novel approach to mitigate these untoward vibrations can be the use of nonlinear absorbers. These act as Nonlinear Energy Sinks (NESs). The NES is coupled to the primary (drivetrain) structure, inducing passive irreversible targeted energy transfer (TET) from the drivetrain system to the NES. During this process, the vibration energy is directed from the lower-frequency modes of the structure to the higher ones. Thereafter, vibrations can be either dissipated through structural damping or consumed by the NES. This paper uses a lumped parameter model of an automotive driveline to simulate the effect of TET and the assumed modal energy redistribution. Significant redistribution of vibratory energy is observed through TET. Furthermore, the integrated optimization process highlights the most effective configuration and parametric evaluation for use of NES.

Roller bearing dynamics under transient thermal-mixed non-Newtonian elastohydrodynamic regime of lubrication

The paper describes a combined tribodynamics analysis (dynamics and contact tribology) of cylindrical roller bearings of a heavy duty truck transmission under high applied loads. The dynamic analysis provides the transient variations in contact load. It also determines the vibration spectrum of the bearing as well as that of contact dynamics. It is shown that with sufficient preloading and/or interference fitting a widely spread loaded region results, which reduces bearing-induced vibration. The transient tribological analysis, including thermal analysis with a novel and realistic lubricant inlet boundary condition demonstrates that non-Newtonian mixed elastohydrodynamic regime of lubrication is prevalent, but with reduced friction compared with unrealistic dry Coulombic friction, which is often assumed in literature.